Subgroups — #31823270

Order 17984.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17985113	C₂	1	1	yes	maximal, characteristic, complemented
2	#22582815	C₂	1	1	yes	maximal, characteristic, complemented
3	#135×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	#17985122	—	2	1	no	—
5	#17985113	—	2	1	no	—
6	#41×C₂₈₁	—	2	1	no	—
7	Q₁₆×C₂₈₁	C₄	1	1	yes	characteristic
8	SD₁₆×C₂₈₁	—	2	1	no	—
9	D₈×C₂₈₁	C₄	1	1	yes	characteristic
10	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
11	#14555886	—	4	1	no	—
12	Q₈×C₂₈₁	—	2	1	no	—
13	D₄×C₂₈₁	—	2	1	no	—
14	D₄×C₂₈₁	—	4	1	no	—
15	C₂×C₄×C₂₈₁	—	4	1	no	—
16	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
17	C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₈₁	D₄	1	1	yes	characteristic
19	C₂²×C₂₈₁	—	4	1	no	—
20	C₂²×C₂₈₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₂₈₁	—	4	1	no	—
22	C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₂₈₁	D₈	1	1	yes	characteristic
24	C₂×C₂₈₁	—	2	1	no	—
25	C₂×C₂₈₁	—	8	1	no	—
26	C₂×C₂₈₁	#102	1	1	yes	characteristic
27	C₂₈₁	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	281	1	no	maximal, Sylow
29	#135	D₂₈₁	1	1	yes	characteristic
30	C₂×C₁₆	—	281	1	no	—
31	#108	—	281	1	no	—
32	#41	—	2	1	no	—
33	Q₁₆	Dic₂₈₁	1	1	yes	characteristic
34	SD₁₆	—	2	1	no	—
35	D₈	Dic₂₈₁	1	1	yes	characteristic
36	M₁₆	—	562	1	no	—
37	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
38	C₁₆	—	562	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	4	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	C₂²⋊D₂₈₁	1	1	yes	characteristic
44	C₈	—	1124	1	no	—
45	C₈	C₂×Dic₂₈₁	1	1	yes	characteristic
46	C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	#17985126	1	1	yes	characteristic
49	C₄	—	4	1	no	—
50	C₄	C₂²⋊Dic₂₈₁	1	1	yes	characteristic
51	C₄	#17985123	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	8	1	no	—
54	C₂	#22582800	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17985123
commutator	C₈×C₂₈₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₈₁
Fitting, prime radical	#135×C₂₈₁	C₂
socle	C₂×C₂₈₁	#102
cosocle	C₂×C₈×C₂₈₁	C₂²
hypercenter	#135	D₂₈₁
hypocenter	C₂₈₁	#359
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#17985113	C₂	semidirect
2. #22582815	C₂	semidirect
27. C₂₈₁	#359	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#17985113	2
#22582815	2
#135×C₂₈₁	2
#359	281